Discussion of flight times and distances on a round earth versus a flat earth

  • 5 Replies
Warning: Long post:

I started a discussion on another flat earth website by challenging any flat earth believer to do a test by circumnavigating the earth on commercial flights that stay within the southern hemisphere. It led to a very involved discussion which I am pasting here in case someone on this forum has more perspectives to offer. Here is the thread from the other website:

I have an experiment which I posted on Eric Dubay's videos and facebook page (I did not realize he is a controversial figure) but here is my proposed experiment as addressed to Mr. Dubay:

I wonder if we could start a crowd funding campaign to buy Eric Dubay a series of plane tickets that would allow him to fly around the world in one easterly direction without ever leaving the southern hemisphere in a fraction of the time that any map of a flat earth would indicate was possible. Here are some flights and flight times taken from Kayak.com that would do the trick:
3:55p — 6:40p
Economy 2h 45m
Buenos Aires (EZE) — São Paulo (GRU)
GOL Linhas Aéreas 7453  ·  Narrow-body jet  ·  Boeing 737-800
Change planes in São Paulo (GRU)  Long layover
4h 55m
11:35p — 1:00p
Lands Sat, Apr 1
Economy 8h 25m
São Paulo (GRU) — Johannesburg (JNB)
South African 225  ·  Wide-body jet  ·  Airbus A330-200

7:10p — 3:55p
Lands Sat, Apr 1
Economy 11h 45m
Johannesburg (JNB) — Sydney (SYD) 2 seats remain
Qantas Airways 64  ·  Wide-body jet  ·  Boeing 747-400

16h 00m
1:50p — 6:55p
Economy 3h 05m
Sydney (SYD) — Auckland (AKL)
Air New Zealand 710  ·  Narrow-body jet  ·  Airbus A320-100/200
Change planes in Auckland (AKL) 
1h 10m
8:05p — 3:50p
Prem 11h 45m
Auckland (AKL) — Buenos Aires (EZE)
Air New Zealand 30  ·  Wide-body jet  ·  Boeing 787-9

Total time in the air is 37 hours and 45 minutes (not counting layovers). With an average speed in the air of say 580 mph (which is very generous given the aircraft being used), this would mean a maximum total distance of 21,895 miles to circumnavigate the globe while staying within the Souuthern Hemisphere. Note that these flights actually includes some north and south deviation which will add distance and time in the air which means this figure is higher than would be absolutely necessary to circumnavigate, but again all of these flights stay entirely within the Southern Hemisphere and so do not cross the equator.

Since both flat earthers and globe earthers agree that the distance around the equator is more than 24,000 miles (flat earth models actually have the distance around the equator as 39,000 miles-see note below), then it should not be possible to circumnavigate the globe within the southern hemisphere while only being in the air for 37 hours and 45 minutes while using modern day commercial aricraft. And it should be even more impossible with a flat earth model where the distance at the southern latitudes of the cities traversed would be much, much greater. Sao Paulo is the northernmost city on this itinerary and is 7991 miles from the North Pole. So the circumference of the earth at that latitude on a flat earth would be over 50, 200 miles.

The question I would pose to Mr. Dubay is "If you personally traveled around the world in a combined flight time of less than 38 hours without leaving the Southern Hemisphere, would you then be willing to admit that the flat earth model you propose is fatally flawed?" If the answer is yes, then maybe we could get a crowd-funding project to buy your tickets and put this whole debate to rest. What do you say, Mr Dubay? Are you willing to test your theory in a real world experiment that cannot be faked and that would allow you to time your own flights, and use whatever means you need to use to determine that you were truly in the cities included on this circumnavigation trip and had stayed within the Southern Hemisphere?

Note regarding the distance around the equator: I found this post on the following page:https://www.theflatearthsociety.org/forum/index.php?topic=59426.0

"A thought occured to me when doing the maths for my ladder experiment: the distance around the equator is drastically different between FE and RE models. Both models use the same equation: C = t*r, but each have a different radius. For RE, the radius is that of the Earth at 6371 km (3,959 mi); for FE it's the distance from the north pole to the equator, roughly 10,009 km (6219 mi).

Thus, RE says the equator is roughly 40,000 km (24,874 mi) while FE says it should be 62,888 km (39,077 mi). In 1986 an historical and well-documented flight took place wherein two people got into an airplane at Edwards Air Force Base and took off. Just over nine days later they landed at Edwards Air Force Base, having circled the Earth more or less about the Equator[1][2] with a total flight distance of 40,212 kilometers (24,987 miles).

Was this a scam? Did the pilots fly a shorter, northern route for nine days instead of sticking to the equator? Or is the FE distance around the equator false?"

It is from these calculations that I came up with the 39,000 mile length of the equator for the flat earth, and then extrpolated based on the distance to Sao Paulo from the North Pole.

Who knows, we might even get some flat earth people to go along and test it with Mr. Dubay. The total cost for the around the world portion of the journey would be under $5000 (there is a cheaper flight from Sydney to Buenos Aries through Santiago). Are there any true believers in the flat earth that would be willing to put their beliefs on the line for $5000? Or are there enough people who are just tired of the arguments back and forth that would be willing to pay for Mr. Dubay to make the trip and settle this question once and for all? I would chip in $100 to such a crowd-funding effort.

The ball is in your court, Mr. Dubay. Are you game to test your own theory?

Note added: Anyone on this website willing to make the journey? At just $5-7000, it would seem like a quick and easy way for the believers in a flat earth to test their theory.

Someone replied: "I would just say that I was in the Southern Hemisphere of the Bi-Polar Flat Earth model."

So I wrote him again and asked:

Using the bipolar map that has been displayed many times on this website, how would you explain the flight times:
Auckland to Buenos Aries 11 hours 45 minutes
Sao Paulo to Johanneburg: 8 hours 25 minutes
When clearly on the bipolar map Aukland is twice as far from Buenos Aries as Sao Paulo is from Johannesburg.
Also there are flights from Sydney to Santiago that take 12 hours and 40 minutes. On the bipolar earth model Sydney to Santiago is around three times as far as Sao Paulo to Johanneburg.
Finally, Sydney to Auckland takes only 3 hours and 5 minutes, and it is TWICE as far as Sao Paulo to Johannesburg on the bipolar map.
Can you explain these glaring differences in flight times versus distance traveled on the bipolar map?

He replied:

"The bipolar map is just a guide for the idea. No one mapped out where the continents would appear."

So I replied to him again with:

So, are you saying that after thousands of years of land and sea travel, and 100 years of air travel, that no one has worked out the location and shape and size of the continents relative to each other in a way that can be accurately represented on a map? We are talking about creating a two dimensional map of the relatively two dimensional surface of a flat earth, and yet the best visual representation of it that you can provide shows Singapore to be over 10,000 miles from Auckland, when I can fly commercially between the two cities in under 10 hours?

This strains credulity to the breaking point and beyond.

I saw claims that this site is just a joke meant to draw people into pointless discussions, and now I think that has got to be the only explanation for the glaring inconsistencies that no flat earther on here can explain.

« Last Edit: April 07, 2017, 03:15:12 PM by Nirmala »

His response: "Maps aren't accurate. Why should we assume that they are? Have you looked at the size of Greenland lately on a Mercator map?"

My reply to him:

No one has ever claimed that a Mercator map was accurate, and in fact it is notoriously inaccurate. That is what happens when you transfer a three dimensional object to two dimensions. It becomes distorted.

However, that would not happen when you represent a two dimensional object on a two dimensional map. There is absolutely no reason why someone cannot create a two-dimensional map of a flat surface that is completely accurate and to scale. That should be a strong point in favor of a flat earth....except that no one has ever been able to accomplish this ridiculously simple task, probably because the object being represented is not two-dimensional or flat.

Distortion matters less in a map of a small area of a sphere, which is why say a map of the state of Florida is pretty accurate in two dimensions. The differences in the third dimension are slight enough to not matter as a practical matter. This is also why Buckminster Fuller's map is roughly accurate in terms of scale

However, there is one form of map that shows a completely accurate representation of the continents, where distances from any two points on earth are completely accurate according to the scale of the map, and according to the observed distance when driving or sailing or flying between those two points. What kind of perfect map is that? It is called a globe! A globe even explains perfectly why in the northern hemisphere, what appears to be a flight path that curves to the north is often the shortest route between two points. Hence the use of northern routes to fly from say Los Angeles to Dubai. If you measure the distance on a globe, the shortest path is over the northern end of Greenland.

So for hundreds of years we have had a map that works perfectly to show the correct distances and now flight times between any two points. It seems fatuous to claim that maps aren't accurate when there is one map that is completely accurate. Unfortunately, it also can be used to prove that the earth is a round ball. Does that seem like a good reason to deny the accuracy of the perfect map? Airlines use this map. Ships use this map. And when I drive across the US, I am actually using the info from the globe to calculate my driving distances, or it would take me much longer than it does in the real world.

If the flat earth was real, there would be a corresponding accurate map. There just is not. Again it seems silly to blame the map makers, when it is the underlying model of reality that is incorrect.

He replied:
Mapping the world is a ridiculously simple task?  ???

Mapping a two dimensional object onto a two dimensional sheet of paper is ridiculously simple....in comparison to mapping a three dimensional object to a two dimensional piece of paper. The latter requires the use of perspective. The former does not. Again, a small enough area makes this obvious, so a blueprint or elevation drawing of a 20,000 square foot building is for all practical purposes completely accurate and does not require the use of perspective techniques. If I want to focus on one corner of the building/blueprint, I just move my eyes over that part of the blueprint to get an accurate sense of the proportions of the rooms in that corner. However an artist's rendering of that same building as it appears from a distance would need to use all of the tricks of perspective to make it look proportional due to the introduction of a third dimension to the drawing (the distance from the artist's eyes to the various parts of the building). So the artist would draw a distant part of the building with smaller dimensions and a nearer part of the building with larger dimensions. If a builder tried to build the building by using the dimensions of the artist's view, the building would be bizarrely proportioned.

Same thing with a map. Any two-dimensional viewpoint of a three dimensional object, like a round planet, will introduce all kinds of distortions. However, a two dimensional drawing of a flat object as seen from above does not have these problems. Even if it is a very large map or drawing, the distances everywhere on the map should correspond to the scale of the map with complete accuracy. No map of the flat earth accomplishes anything close to this simple task. All of the distances are known and have been measured on the surface of the earth or in the air in numerous surveys. All the map maker would need to do if the earth was flat is enter all of those distances. Someone on youtube actually tried to do this with the flat earth map by adjusting it to show distances that correspond to actual flight times: Unfortunately, he was unable to adjust his map to take into account all of the flight times and distances. To check this,you just need to look at some of the flights I have already mentioned, i.e. Sydney to Johannesburg versus Sydney to Santiago. Or you can just look at the flight from Sydney to Perth and realize his map is grossly inaccurate. On his map, the distance from Sydney to Perth is much greater than the distance from the Panama Canal to the north pole.

If the flat earth was real, there would be a corresponding accurate map. There just is not. Again it seems silly to blame the map makers, when it is the underlying model of reality that is incorrect.

His responses: Sorry, but I don't see how anything of you said really has mapping the world trivially easy.
Please provide us the database of the measured distances between every point on earth if you think that all of this exists somewhere. This is the second time I have asked.
Navigators sure seem to have been using these inaccurate maps to navigate the world for hundreds of years. What makes you think that they could not use an inaccurate globe?
It appears that you merely went to Kyak.com and got some flight estimates. How do we know that those estimates will meet reality? 1 out of 4 flights are delayed.
Again, please show us where these accurate measurements have taken place.

I clarified that mapping a flat earth would be much easier because you are mapping a relatively two-dimensional object. As you say, these maps have been around for hundreds of years. It would seem that someone would have gotten it right by now, if indeed they were mapping a two dimensional object.

As for navigation, for hundreds of years navigators have taken into account the distortions in their maps. This is from a Britannica.com article about navigation charts: "In 1599 the English mathematician Edward Wright supplied a rational explanation of Mercator’s projection and provided tables by which the distorted distances could be corrected."

I could not find a single database for the entire earth, but I found this site that will tell you driving distances on Australia, which I picked because it is so distorted on every flat earth map I have seen: https://www.timeanddate.com/worldclock/distanceresult.html?p1=240&p2=196
The results for driving from Sydney to Perth come out at 3934 km which follows roads and wisely avoids traversing water
I also found this calculator for calculating distances which is based on a round earth:
It calculated and displayed a slightly curved path from Sydney to Perth that measures 3298 km which makes sense given no roads are involved.
Quantas has a Flight Aware tracking system for flight # 581 from Sydney to Perth showing a flight distance of 3281 km (2039 miles) with expected average flight speed of 409 mph:
You will see on that page that the last 14 flights all arrived within 5 hours of departure except one which was 5 hours and 2 minutes.

These are all calculations based on a round earth and they are incredibly accurate. I challenge you to show me a map based on a flat earth that comes even remotely close to these calculations. A globe does allow these calculations to work, but so do map projections based on a round earth that are biased to show the continents in their correct relative sizes such as the Dymaxion map by Buckminster Fuller or the Authagraph projection (note that the best way to do this is to cut the earth up into triangles which can be flattened out and then also can be folded back up to make a roughly spherical shaped globe).

The reason these calculations do not work based on a flat earth model is simple, the earth is not flat. That also explains why the flight path in the link above curves south over the water. A straight line on a two dimensional map does not take into account the curvature of the earth. I am pretty sure the airlines would not fly hundreds of miles out of their way just to support a conspiracy to keep us all in the dark about the shape of the earth.

 I found two more relevant links. The first is a description of how great circle distances are calculated using the geometry of a sphere: https://en.wikipedia.org/wiki/Great-circle_distance Note that these distance calculations only work on the surface of a sphere.

The second link is a website with a database of 1000 air routes using the great circle distances: http://www.greatcirclemapper.net/en/routes.html
Note that the site also allows you to calculate the great circle distance between any two airports using the spherical model of the earth.

The second website gave the calculation for Sydney to Perth as 3284 km which is what the earlier websites also predicted, and what Quantas flies every day. You can use the flight tracking system to check historical records of hundreds if not thousands of flight times distances on Quantas. I did not search other airlines, but they may have similar databases. Correction: The flight tracker website showing the Quantas data has similar data for over 10,000 operators of aircraft, so you should be able to check any airline and any route on there and find a historical record of flight times and the calculated distance and expected speed. So you asked for a large database of historical records of distances traveled, and I have now provided you with one that probably has millions of historical records of actual flights flown by commercial aircraft of all types.

Maybe the reason there is no database for every two points on the earth is that there is no need for one when you can so easily calculate the data using a spherical model of the earth. Here is another calculator that allows you to calculate based on the latitude and longitude of any two points: http://www.nhc.noaa.gov/gccalc.shtml

What method or methods do you propose for calculating distances on a flat earth? If the earth is truly flat, these calculations should be fairly simple as they would all involve just two dimensions instead of three. No matter what the actual outline or shape is of the flat earth, you could simply lay a right angle grid over it and thereby calculate all of the distances from any two points within that grid using the simplest geometry of right triangles. Can you show me any such examples of a grid showing these kind of coordinates? Are there any calculators for a flat earth that even cover say one hemisphere? The spherical earth has such a system of coordinates known as latitude and longitude, but they are not aligned at right angles due to the spherical model....and yet they work in every test case. It should be easy to create such a grid on a flat earth and yet no one has done so. Why is that? Can you show me any examples where calculations from a grid on a map of the flat earth matched up with actual flight paths and times? If not, why not, when round earth calculators are so common and accurate?

You keep asking me for data, and I have offered some. I have not seen any data from you that supports a different arrangement of the continents or a different calculation or measurement of the distances between well known airports based on a flat earth. Can you give me just one example? And if you do offer such an example, does it contradict any other possible calculations, such as on the map I shared where some air routes are correct, but others are not? I have offered examples on both the unipolar and bipolar maps where the route distances  versus the flight times are incorrect. Can you show me one example where the distance calculated on a sphere using the calculators linked to above do not correspond to actual flight times? It seems I have offered a lot of data. Maybe it is your turn
« Last Edit: March 28, 2017, 02:13:04 PM by Nirmala »

I added some more to the other thread:

I would be very open to it if any flat earther could show me a world map that does work with the air travel data in the links I shared. But it seems pretty obvious that this would have already happened if the earth were truly flat. It is a bit mind boggling to think that in this day and age someone could suggest that no one is able to draw an accurate map of the surface of our planet, when it has been traversed so many millions of times. I found a source online that suggests that 102,465 commercial airline flights occur each and every day covering 49,871 regularly scheduled routes. In 2014 that worked out to 37.4 million flights, which does not even include private aircraft and military flights. How is it possible that all of those pilots seem to be arriving at their destinations according to the flight paths worked out using spherical geometry? And really, why would there not be detailed maps at least of all of the most populated areas and major air routes over the ocean that could be pieced together into a relatively accurate map of this supposed flat earth, if in fact those millions of flights were over a relatively flat earth? Are all commercial, military and private pilots in on this grand conspiracy to deceive the rest of us into believing that the earth is round?

And wouldn't a lot of passengers have complained by now if all of the flights in the southern hemisphere took much longer than the airlines say they should take and are actually being flown each and every day? I saw a youtube video where someone claimed that these flights are scheduled but never actually happen. Don't you think thousands of travelers would have complained by now that they are unable to book regularly scheduled flights listed on multiple airlines and flight booking sites? I personally have flown from Sydney to Perth, and it took about 5 hours. Where are all of the other stymied travelers who are not getting where they want to go, or who are landing hours and hours later than they were promised?

The typical flat earth map is what is called a Polar Azimuthal Equidistant Projection. As described on Wikipedia, "It has the useful properties that all points on the map are at proportionately correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection. It is useful for showing airline distances from center point of projection and for seismic and radio work."

So it shows fairly accurate distances for north/south airline flights in the Northern Hemisphere including all great circle flights that go near the north pole, as those flights would travel generally north and then generally south, such as Los Angeles to Dubai. And if you plot these flights on this kind of map, distances and the path flown are pretty close to being accurate. Flights due east or west would be less accurate and more so as you move further away from the pole. Once you reach the Southern Hemisphere, then east /west distances are all messed up. This is why continents in the Northern Hemisphere look pretty porportional to their actual shape. Then as you approach and cross the equator to the south, things get more and more messed up which is why South America and Australia look so disproportional to the shape they would be if you measured them from the air (you can use the flight tracker linked to above to check this, and Sydney to Perth is the easiest example to check).

Just for fun, on the following page is a Polar Azimuthal Equidistant Projection using the South Pole as the center point: https://probaway.wordpress.com/2008/11/02/the-gene-barrel-distribution-around-the-south-pole/

And guess what? Now everything stated above is still true if you simply swap the words North and South. Continents and flight paths in the Southern Hemisphere suddenly look relatively correct and the continents and flight paths in the North are all messed up....and I mean really messed up!!

I am not surprised that  no one has argued for a flat earth with the south pole at the center! And this is true, even though many other aspects of the flat earth model would work almost as well such as the path of the sun and moon in the sky. Luckily for flat earth proponents, most of the earth's population lives in the Northern Hemisphere, so the gross discrepancies in their map do not jump out at people who are north-centric in their worldview.

It is also ironic that the main map used by flat earth proponents is actually created by projecting the earth as it appears on a globe onto a flat surface. Their own map is based on a globe! The bipolar map is a Gott-Mugnolo Azimuthal projection which is a similar projection taken with a point on the equator as the center, and while it does correct some distances, it also has distortions and also is a projection taken from a globe!!

Can't the flat earthers come up with their own map without cheating off of the globe?

Can't the flat earthers come up with their own map without cheating off of the globe?


I found another website where someone did some similar calculations regarding flight times versus distances on a globe and a flat earth map: http://creation.com/a-direct-test-of-the-flat-earth-model-flight-times

Interestingly, it is a Christian website. Also, the author of the article states in the comments that he and several other people who work in his ministry have personally flown many of the routes he used and so can personally verify that the flight times are correct.

I also noticed that he did not include the Sydney to Santiago (Australia to South America) route. If he had the flat earth data would have been even more erroneous, as that is where the greatest distortion in distances would have been measured. He included several routes that are mostly north/south routes. There is little or no distortion of distances along lines of longitude in the flat earth map, so those routes would be accurately measured on both a globe and flat earth map.